Syllabus

Tiedoston sisältö

FYSP120 Fysiikan Numeeriset menetelmt / numerical methods in physics

SYLLABUS
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- GENERAL: Matlab and/or octave
- Approximation of data : least squares fit
  - spline interpolation
  - Pade approximants
  - Fourier series and FFT
  - B-spline basis functions
- Numerical Integration
  - Newton-Cotes quadratures
     - Simpson rules 
     - derivation of quadratures
  - Adaptive integration routines
  - Gauss quadratures
    - derivation
- Zeros of a real function
  - Newton bisection and Newton-Raphson methods
- Optimization
  - downhill simplex emthod (Nelder and Mead)
  - Steepest descent
  - Newton's method
  - Levenberg-Marquardt method
  - Trust region algorithms (Dog Leg algorithm)
- Differential equations
  - Coupled diff. equations
  - Stiff set of equations; implicit Euler method
  - 4th order Runge-Kutta method
- Eigenvalue equations
  - Power method
  - Krylov subsspace: Arnoldi and Lanczos iterations
  - B-spline solution of Schrdinger equation
- Simulations
  - Molecular dynamics
  - Variational Monte Carlo
     - Metropolis algorithm 
     - detailed balance 
     - Markov chains
     - Statistical independence and error estimation